Question 390342
If the 1st year was {{{x}}}
after 1 year {{{.7x}}}
after 2 years {{{.7*.7x}}}
after 3 years {{{.7*.7*.7x}}}
The general formula would be:
{{{.7^n * x}}}   = dollars of value after {{{n}}} years
{{{.7^n *15000 = 500}}}
{{{.7^n = 500/15000}}}
{{{.7^n = 1/30}}}
Take the log of both sides
{{{n*log(.7) = -log(30)}}}
{{{n = (-log(30))/log(.7)}}}
{{{n = (-1.477)/ (-.1549) = 9.535}}}
About 9 years, 6 months and 13 days